Inference Rule with Quantifier and implication

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The discussion revolves around the logical implications of the statements regarding healthy food and taste. It establishes that since all healthy food does not taste good, and spinach is healthy, Duncan does not eat spinach because he prefers tasty food. The argument clarifies that one cannot conclude that hamburgers are tasty or that Duncan eats them based on the provided premises. It emphasizes that the statement about healthy food does not imply that unhealthy food is tasty. The key conclusion is that the premises lead to the understanding that Duncan avoids spinach due to its lack of taste.
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Homework Statement


All healthy food does not taste good. "
Spinach is a healthy food. Duncan only want to eat tasty food. Duncan does not eat spinach. Hamburger is not a healthy food.
Write all possible conclusion.
I try to translate it into proposition with quantifier, such as t(x)=x is tasty, h(x)=x is healthy, d(x)= Doddy eats x.

The Attempt at a Solution



I think d(hamburger) is not a conclusion because the argument is d(x) \rightarrow t(x). We cannot conclude d(hamburger) or t(hamburger), because proposition said h(x) \rightarrow ~t(x) and d(x) \rightarrow t(x). Is it right?
 
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Yes, that is correct. (Assuming that "Doddy" is a nickname for "Duncan"!) Saying "All healthy food does not taste good" does NOT imply that unhealthy food does taste good. Of course, "not d(spinach)" would be a conclusion from the first two statements but that is given as the third statement.
 

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